The width of a rectangle

Question

The width of a rectangle is 3 feet less than the length. The area is 108 square feet. Find the dimensions of the rectangle algebraically.

Answer 1

A = 108 = L× W

W = L – 3 so L× (L – 3) = L² – 3L = 108

So we subtract 108 from both sides, the find L by solving the quadratic

L² – 3L – 108 = 0 which can be factored to get

(L – 12)(L + 3) = 0 where L = 12 is the only positive solution

W = L – 3 = 12 – 3 = 9

Answer

The dimensions of the rectangle are

L: 12 ft

W: 9 ft